【坑】ORB特征点提取 描述符计算 暴力匹配

坑：主要在三个地方

1.    这里x^p y^q 中的x，y OpenCV 源码中是所选图像块的坐标，并不是 图形块在整个图像上的坐标；

2.描述符计算时，是将pattern中的点恢复到“真值”坐标在旋转，还是旋转后在恢复到“真值”？应该是旋转之后再恢复到真值；

3，暴力匹配时 注意规避 描述符为空的点；

#include <opencv2/opencv.hpp>

#include <string>

using namespace std;

// global variables
string first_file = "./1.png";
string second_file = "./2.png";

const double pi = 3.1415926;    // pi


// TODO implement this function
/**
 * compute the angle for ORB descriptor
 * @param [in] image input image
 * @param [in|out] detected keypoints
 */
void computeAngle(const cv::Mat &image, vector<cv::KeyPoint> &keypoints);

// TODO implement this function
/**
 * compute ORB descriptor
 * @param [in] image the input image
 * @param [in] keypoints detected keypoints
 * @param [out] desc descriptor
 */
typedef vector<bool> DescType;  // type of descriptor, 256 bools
void computeORBDesc(const cv::Mat &image, vector<cv::KeyPoint> &keypoints, vector<DescType> &desc);

// TODO implement this function
/**
 * brute-force match two sets of descriptors
 * @param desc1 the first descriptor
 * @param desc2 the second descriptor
 * @param matches matches of two images
 */
void bfMatch(const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches);

int main(int argc, char **argv) {

    // load image
    cv::Mat first_image = cv::imread(first_file, 0);    // load grayscale image
    cv::Mat second_image = cv::imread(second_file, 0);  // load grayscale image

    // plot the image
    cv::imshow("first image", first_image);
    cv::imshow("second image", second_image);
    cv::waitKey(0);

    // detect FAST keypoints using threshold=40
    vector<cv::KeyPoint> keypoints;
    cv::FAST(first_image, keypoints, 40);
    cout << "keypoints: " << keypoints.size() << endl;

    // compute angle for each keypoint
    computeAngle(first_image, keypoints);

    // compute ORB descriptors
    vector<DescType> descriptors;
    computeORBDesc(first_image, keypoints, descriptors);

    // plot the keypoints
    cv::Mat image_show;
    cv::drawKeypoints(first_image, keypoints, image_show, cv::Scalar::all(-1),
                      cv::DrawMatchesFlags::DRAW_RICH_KEYPOINTS);
    cv::imshow("features", image_show);
    cv::imwrite("feat1.png", image_show);
    cv::waitKey(0);

    // we can also match descriptors between images
    // same for the second
    vector<cv::KeyPoint> keypoints2;
    cv::FAST(second_image, keypoints2, 40);
    cout << "keypoints: " << keypoints2.size() << endl;

    // compute angle for each keypoint
    computeAngle(second_image, keypoints2);

    // compute ORB descriptors
    vector<DescType> descriptors2;
    computeORBDesc(second_image, keypoints2, descriptors2);

    // find matches
    vector<cv::DMatch> matches;
    bfMatch(descriptors, descriptors2, matches);
    cout << "matches: " << matches.size() << endl;

    // plot the matches
    cv::drawMatches(first_image, keypoints, second_image, keypoints2, matches, image_show);
    cv::imshow("matches", image_show);
    cv::imwrite("matches.png", image_show);
    cv::waitKey(0);

    cout << "done." << endl;
    return 0;
}

// -------------------------------------------------------------------------------------------------- //

// compute the angle
void computeAngle(const cv::Mat &image, vector<cv::KeyPoint> &keypoints) {
    int half_patch_size = 8;
    for (auto &kp : keypoints) {
    // START YOUR CODE HERE (~7 lines)
//        kp.angle = 0; // compute kp.angle
        double m10 = 0;
        double m01 = 0;
        int x =cvRound(kp.pt.x);
        int y =cvRound(kp.pt.y);
        if(x-half_patch_size<0||x+half_patch_size>image.cols||
           y-half_patch_size<0||y+half_patch_size>image.rows)
            continue;
        for(int u = x - half_patch_size;u<x + half_patch_size;++u)
        {
            for(int v = y -half_patch_size;v< y + half_patch_size;++v)
            {
                m10 +=  (u-x)*image.at<uchar>(v,u);
                m01 +=  (v-y)*image.at<uchar>(v,u);
            }
        }

        double theta = std::atan(m01/m10);
        kp.angle = theta * 180/pi;
        cout<<"kp.angel:"<<kp.angle<<endl;
//         END YOUR CODE HERE
    }
    return;
}

// -------------------------------------------------------------------------------------------------- //
// ORB pattern
int ORB_pattern[256 * 4] = {
        8, -3, 9, 5/*mean (0), correlation (0)*/,
        4, 2, 7, -12/*mean (1.12461e-05), correlation (0.0437584)*/,
        -11, 9, -8, 2/*mean (3.37382e-05), correlation (0.0617409)*/,
        7, -12, 12, -13/*mean (5.62303e-05), correlation (0.0636977)*/,
        2, -13, 2, 12/*mean (0.000134953), correlation (0.085099)*/,
        1, -7, 1, 6/*mean (0.000528565), correlation (0.0857175)*/,
        -2, -10, -2, -4/*mean (0.0188821), correlation (0.0985774)*/,
        -13, -13, -11, -8/*mean (0.0363135), correlation (0.0899616)*/,
        -13, -3, -12, -9/*mean (0.121806), correlation (0.099849)*/,
        10, 4, 11, 9/*mean (0.122065), correlation (0.093285)*/,
        -13, -8, -8, -9/*mean (0.162787), correlation (0.0942748)*/,
        -11, 7, -9, 12/*mean (0.21561), correlation (0.0974438)*/,
        7, 7, 12, 6/*mean (0.160583), correlation (0.130064)*/,
        -4, -5, -3, 0/*mean (0.228171), correlation (0.132998)*/,
        -13, 2, -12, -3/*mean (0.00997526), correlation (0.145926)*/,
        -9, 0, -7, 5/*mean (0.198234), correlation (0.143636)*/,
        12, -6, 12, -1/*mean (0.0676226), correlation (0.16689)*/,
        -3, 6, -2, 12/*mean (0.166847), correlation (0.171682)*/,
        -6, -13, -4, -8/*mean (0.101215), correlation (0.179716)*/,
        11, -13, 12, -8/*mean (0.200641), correlation (0.192279)*/,
        4, 7, 5, 1/*mean (0.205106), correlation (0.186848)*/,
        5, -3, 10, -3/*mean (0.234908), correlation (0.192319)*/,
        3, -7, 6, 12/*mean (0.0709964), correlation (0.210872)*/,
        -8, -7, -6, -2/*mean (0.0939834), correlation (0.212589)*/,
        -2, 11, -1, -10/*mean (0.127778), correlation (0.20866)*/,
        -13, 12, -8, 10/*mean (0.14783), correlation (0.206356)*/,
        -7, 3, -5, -3/*mean (0.182141), correlation (0.198942)*/,
        -4, 2, -3, 7/*mean (0.188237), correlation (0.21384)*/,
        -10, -12, -6, 11/*mean (0.14865), correlation (0.23571)*/,
        5, -12, 6, -7/*mean (0.222312), correlation (0.23324)*/,
        5, -6, 7, -1/*mean (0.229082), correlation (0.23389)*/,
        1, 0, 4, -5/*mean (0.241577), correlation (0.215286)*/,
        9, 11, 11, -13/*mean (0.00338507), correlation (0.251373)*/,
        4, 7, 4, 12/*mean (0.131005), correlation (0.257622)*/,
        2, -1, 4, 4/*mean (0.152755), correlation (0.255205)*/,
        -4, -12, -2, 7/*mean (0.182771), correlation (0.244867)*/,
        -8, -5, -7, -10/*mean (0.186898), correlation (0.23901)*/,
        4, 11, 9, 12/*mean (0.226226), correlation (0.258255)*/,
        0, -8, 1, -13/*mean (0.0897886), correlation (0.274827)*/,
        -13, -2, -8, 2/*mean (0.148774), correlation (0.28065)*/,
        -3, -2, -2, 3/*mean (0.153048), correlation (0.283063)*/,
        -6, 9, -4, -9/*mean (0.169523), correlation (0.278248)*/,
        8, 12, 10, 7/*mean (0.225337), correlation (0.282851)*/,
        0, 9, 1, 3/*mean (0.226687), correlation (0.278734)*/,
        7, -5, 11, -10/*mean (0.00693882), correlation (0.305161)*/,
        -13, -6, -11, 0/*mean (0.0227283), correlation (0.300181)*/,
        10, 7, 12, 1/*mean (0.125517), correlation (0.31089)*/,
        -6, -3, -6, 12/*mean (0.131748), correlation (0.312779)*/,
        10, -9, 12, -4/*mean (0.144827), correlation (0.292797)*/,
        -13, 8, -8, -12/*mean (0.149202), correlation (0.308918)*/,
        -13, 0, -8, -4/*mean (0.160909), correlation (0.310013)*/,
        3, 3, 7, 8/*mean (0.177755), correlation (0.309394)*/,
        5, 7, 10, -7/*mean (0.212337), correlation (0.310315)*/,
        -1, 7, 1, -12/*mean (0.214429), correlation (0.311933)*/,
        3, -10, 5, 6/*mean (0.235807), correlation (0.313104)*/,
        2, -4, 3, -10/*mean (0.00494827), correlation (0.344948)*/,
        -13, 0, -13, 5/*mean (0.0549145), correlation (0.344675)*/,
        -13, -7, -12, 12/*mean (0.103385), correlation (0.342715)*/,
        -13, 3, -11, 8/*mean (0.134222), correlation (0.322922)*/,
        -7, 12, -4, 7/*mean (0.153284), correlation (0.337061)*/,
        6, -10, 12, 8/*mean (0.154881), correlation (0.329257)*/,
        -9, -1, -7, -6/*mean (0.200967), correlation (0.33312)*/,
        -2, -5, 0, 12/*mean (0.201518), correlation (0.340635)*/,
        -12, 5, -7, 5/*mean (0.207805), correlation (0.335631)*/,
        3, -10, 8, -13/*mean (0.224438), correlation (0.34504)*/,
        -7, -7, -4, 5/*mean (0.239361), correlation (0.338053)*/,
        -3, -2, -1, -7/*mean (0.240744), correlation (0.344322)*/,
        2, 9, 5, -11/*mean (0.242949), correlation (0.34145)*/,
        -11, -13, -5, -13/*mean (0.244028), correlation (0.336861)*/,
        -1, 6, 0, -1/*mean (0.247571), correlation (0.343684)*/,
        5, -3, 5, 2/*mean (0.000697256), correlation (0.357265)*/,
        -4, -13, -4, 12/*mean (0.00213675), correlation (0.373827)*/,
        -9, -6, -9, 6/*mean (0.0126856), correlation (0.373938)*/,
        -12, -10, -8, -4/*mean (0.0152497), correlation (0.364237)*/,
        10, 2, 12, -3/*mean (0.0299933), correlation (0.345292)*/,
        7, 12, 12, 12/*mean (0.0307242), correlation (0.366299)*/,
        -7, -13, -6, 5/*mean (0.0534975), correlation (0.368357)*/,
        -4, 9, -3, 4/*mean (0.099865), correlation (0.372276)*/,
        7, -1, 12, 2/*mean (0.117083), correlation (0.364529)*/,
        -7, 6, -5, 1/*mean (0.126125), correlation (0.369606)*/,
        -13, 11, -12, 5/*mean (0.130364), correlation (0.358502)*/,
        -3, 7, -2, -6/*mean (0.131691), correlation (0.375531)*/,
        7, -8, 12, -7/*mean (0.160166), correlation (0.379508)*/,
        -13, -7, -11, -12/*mean (0.167848), correlation (0.353343)*/,
        1, -3, 12, 12/*mean (0.183378), correlation (0.371916)*/,
        2, -6, 3, 0/*mean (0.228711), correlation (0.371761)*/,
        -4, 3, -2, -13/*mean (0.247211), correlation (0.364063)*/,
        -1, -13, 1, 9/*mean (0.249325), correlation (0.378139)*/,
        7, 1, 8, -6/*mean (0.000652272), correlation (0.411682)*/,
        1, -1, 3, 12/*mean (0.00248538), correlation (0.392988)*/,
        9, 1, 12, 6/*mean (0.0206815), correlation (0.386106)*/,
        -1, -9, -1, 3/*mean (0.0364485), correlation (0.410752)*/,
        -13, -13, -10, 5/*mean (0.0376068), correlation (0.398374)*/,
        7, 7, 10, 12/*mean (0.0424202), correlation (0.405663)*/,
        12, -5, 12, 9/*mean (0.0942645), correlation (0.410422)*/,
        6, 3, 7, 11/*mean (0.1074), correlation (0.413224)*/,
        5, -13, 6, 10/*mean (0.109256), correlation (0.408646)*/,
        2, -12, 2, 3/*mean (0.131691), correlation (0.416076)*/,
        3, 8, 4, -6/*mean (0.165081), correlation (0.417569)*/,
        2, 6, 12, -13/*mean (0.171874), correlation (0.408471)*/,
        9, -12, 10, 3/*mean (0.175146), correlation (0.41296)*/,
        -8, 4, -7, 9/*mean (0.183682), correlation (0.402956)*/,
        -11, 12, -4, -6/*mean (0.184672), correlation (0.416125)*/,
        1, 12, 2, -8/*mean (0.191487), correlation (0.386696)*/,
        6, -9, 7, -4/*mean (0.192668), correlation (0.394771)*/,
        2, 3, 3, -2/*mean (0.200157), correlation (0.408303)*/,
        6, 3, 11, 0/*mean (0.204588), correlation (0.411762)*/,
        3, -3, 8, -8/*mean (0.205904), correlation (0.416294)*/,
        7, 8, 9, 3/*mean (0.213237), correlation (0.409306)*/,
        -11, -5, -6, -4/*mean (0.243444), correlation (0.395069)*/,
        -10, 11, -5, 10/*mean (0.247672), correlation (0.413392)*/,
        -5, -8, -3, 12/*mean (0.24774), correlation (0.411416)*/,
        -10, 5, -9, 0/*mean (0.00213675), correlation (0.454003)*/,
        8, -1, 12, -6/*mean (0.0293635), correlation (0.455368)*/,
        4, -6, 6, -11/*mean (0.0404971), correlation (0.457393)*/,
        -10, 12, -8, 7/*mean (0.0481107), correlation (0.448364)*/,
        4, -2, 6, 7/*mean (0.050641), correlation (0.455019)*/,
        -2, 0, -2, 12/*mean (0.0525978), correlation (0.44338)*/,
        -5, -8, -5, 2/*mean (0.0629667), correlation (0.457096)*/,
        7, -6, 10, 12/*mean (0.0653846), correlation (0.445623)*/,
        -9, -13, -8, -8/*mean (0.0858749), correlation (0.449789)*/,
        -5, -13, -5, -2/*mean (0.122402), correlation (0.450201)*/,
        8, -8, 9, -13/*mean (0.125416), correlation (0.453224)*/,
        -9, -11, -9, 0/*mean (0.130128), correlation (0.458724)*/,
        1, -8, 1, -2/*mean (0.132467), correlation (0.440133)*/,
        7, -4, 9, 1/*mean (0.132692), correlation (0.454)*/,
        -2, 1, -1, -4/*mean (0.135695), correlation (0.455739)*/,
        11, -6, 12, -11/*mean (0.142904), correlation (0.446114)*/,
        -12, -9, -6, 4/*mean (0.146165), correlation (0.451473)*/,
        3, 7, 7, 12/*mean (0.147627), correlation (0.456643)*/,
        5, 5, 10, 8/*mean (0.152901), correlation (0.455036)*/,
        0, -4, 2, 8/*mean (0.167083), correlation (0.459315)*/,
        -9, 12, -5, -13/*mean (0.173234), correlation (0.454706)*/,
        0, 7, 2, 12/*mean (0.18312), correlation (0.433855)*/,
        -1, 2, 1, 7/*mean (0.185504), correlation (0.443838)*/,
        5, 11, 7, -9/*mean (0.185706), correlation (0.451123)*/,
        3, 5, 6, -8/*mean (0.188968), correlation (0.455808)*/,
        -13, -4, -8, 9/*mean (0.191667), correlation (0.459128)*/,
        -5, 9, -3, -3/*mean (0.193196), correlation (0.458364)*/,
        -4, -7, -3, -12/*mean (0.196536), correlation (0.455782)*/,
        6, 5, 8, 0/*mean (0.1972), correlation (0.450481)*/,
        -7, 6, -6, 12/*mean (0.199438), correlation (0.458156)*/,
        -13, 6, -5, -2/*mean (0.211224), correlation (0.449548)*/,
        1, -10, 3, 10/*mean (0.211718), correlation (0.440606)*/,
        4, 1, 8, -4/*mean (0.213034), correlation (0.443177)*/,
        -2, -2, 2, -13/*mean (0.234334), correlation (0.455304)*/,
        2, -12, 12, 12/*mean (0.235684), correlation (0.443436)*/,
        -2, -13, 0, -6/*mean (0.237674), correlation (0.452525)*/,
        4, 1, 9, 3/*mean (0.23962), correlation (0.444824)*/,
        -6, -10, -3, -5/*mean (0.248459), correlation (0.439621)*/,
        -3, -13, -1, 1/*mean (0.249505), correlation (0.456666)*/,
        7, 5, 12, -11/*mean (0.00119208), correlation (0.495466)*/,
        4, -2, 5, -7/*mean (0.00372245), correlation (0.484214)*/,
        -13, 9, -9, -5/*mean (0.00741116), correlation (0.499854)*/,
        7, 1, 8, 6/*mean (0.0208952), correlation (0.499773)*/,
        7, -8, 7, 6/*mean (0.0220085), correlation (0.501609)*/,
        -7, -4, -7, 1/*mean (0.0233806), correlation (0.496568)*/,
        -8, 11, -7, -8/*mean (0.0236505), correlation (0.489719)*/,
        -13, 6, -12, -8/*mean (0.0268781), correlation (0.503487)*/,
        2, 4, 3, 9/*mean (0.0323324), correlation (0.501938)*/,
        10, -5, 12, 3/*mean (0.0399235), correlation (0.494029)*/,
        -6, -5, -6, 7/*mean (0.0420153), correlation (0.486579)*/,
        8, -3, 9, -8/*mean (0.0548021), correlation (0.484237)*/,
        2, -12, 2, 8/*mean (0.0616622), correlation (0.496642)*/,
        -11, -2, -10, 3/*mean (0.0627755), correlation (0.498563)*/,
        -12, -13, -7, -9/*mean (0.0829622), correlation (0.495491)*/,
        -11, 0, -10, -5/*mean (0.0843342), correlation (0.487146)*/,
        5, -3, 11, 8/*mean (0.0929937), correlation (0.502315)*/,
        -2, -13, -1, 12/*mean (0.113327), correlation (0.48941)*/,
        -1, -8, 0, 9/*mean (0.132119), correlation (0.467268)*/,
        -13, -11, -12, -5/*mean (0.136269), correlation (0.498771)*/,
        -10, -2, -10, 11/*mean (0.142173), correlation (0.498714)*/,
        -3, 9, -2, -13/*mean (0.144141), correlation (0.491973)*/,
        2, -3, 3, 2/*mean (0.14892), correlation (0.500782)*/,
        -9, -13, -4, 0/*mean (0.150371), correlation (0.498211)*/,
        -4, 6, -3, -10/*mean (0.152159), correlation (0.495547)*/,
        -4, 12, -2, -7/*mean (0.156152), correlation (0.496925)*/,
        -6, -11, -4, 9/*mean (0.15749), correlation (0.499222)*/,
        6, -3, 6, 11/*mean (0.159211), correlation (0.503821)*/,
        -13, 11, -5, 5/*mean (0.162427), correlation (0.501907)*/,
        11, 11, 12, 6/*mean (0.16652), correlation (0.497632)*/,
        7, -5, 12, -2/*mean (0.169141), correlation (0.484474)*/,
        -1, 12, 0, 7/*mean (0.169456), correlation (0.495339)*/,
        -4, -8, -3, -2/*mean (0.171457), correlation (0.487251)*/,
        -7, 1, -6, 7/*mean (0.175), correlation (0.500024)*/,
        -13, -12, -8, -13/*mean (0.175866), correlation (0.497523)*/,
        -7, -2, -6, -8/*mean (0.178273), correlation (0.501854)*/,
        -8, 5, -6, -9/*mean (0.181107), correlation (0.494888)*/,
        -5, -1, -4, 5/*mean (0.190227), correlation (0.482557)*/,
        -13, 7, -8, 10/*mean (0.196739), correlation (0.496503)*/,
        1, 5, 5, -13/*mean (0.19973), correlation (0.499759)*/,
        1, 0, 10, -13/*mean (0.204465), correlation (0.49873)*/,
        9, 12, 10, -1/*mean (0.209334), correlation (0.49063)*/,
        5, -8, 10, -9/*mean (0.211134), correlation (0.503011)*/,
        -1, 11, 1, -13/*mean (0.212), correlation (0.499414)*/,
        -9, -3, -6, 2/*mean (0.212168), correlation (0.480739)*/,
        -1, -10, 1, 12/*mean (0.212731), correlation (0.502523)*/,
        -13, 1, -8, -10/*mean (0.21327), correlation (0.489786)*/,
        8, -11, 10, -6/*mean (0.214159), correlation (0.488246)*/,
        2, -13, 3, -6/*mean (0.216993), correlation (0.50287)*/,
        7, -13, 12, -9/*mean (0.223639), correlation (0.470502)*/,
        -10, -10, -5, -7/*mean (0.224089), correlation (0.500852)*/,
        -10, -8, -8, -13/*mean (0.228666), correlation (0.502629)*/,
        4, -6, 8, 5/*mean (0.22906), correlation (0.498305)*/,
        3, 12, 8, -13/*mean (0.233378), correlation (0.503825)*/,
        -4, 2, -3, -3/*mean (0.234323), correlation (0.476692)*/,
        5, -13, 10, -12/*mean (0.236392), correlation (0.475462)*/,
        4, -13, 5, -1/*mean (0.236842), correlation (0.504132)*/,
        -9, 9, -4, 3/*mean (0.236977), correlation (0.497739)*/,
        0, 3, 3, -9/*mean (0.24314), correlation (0.499398)*/,
        -12, 1, -6, 1/*mean (0.243297), correlation (0.489447)*/,
        3, 2, 4, -8/*mean (0.00155196), correlation (0.553496)*/,
        -10, -10, -10, 9/*mean (0.00239541), correlation (0.54297)*/,
        8, -13, 12, 12/*mean (0.0034413), correlation (0.544361)*/,
        -8, -12, -6, -5/*mean (0.003565), correlation (0.551225)*/,
        2, 2, 3, 7/*mean (0.00835583), correlation (0.55285)*/,
        10, 6, 11, -8/*mean (0.00885065), correlation (0.540913)*/,
        6, 8, 8, -12/*mean (0.0101552), correlation (0.551085)*/,
        -7, 10, -6, 5/*mean (0.0102227), correlation (0.533635)*/,
        -3, -9, -3, 9/*mean (0.0110211), correlation (0.543121)*/,
        -1, -13, -1, 5/*mean (0.0113473), correlation (0.550173)*/,
        -3, -7, -3, 4/*mean (0.0140913), correlation (0.554774)*/,
        -8, -2, -8, 3/*mean (0.017049), correlation (0.55461)*/,
        4, 2, 12, 12/*mean (0.01778), correlation (0.546921)*/,
        2, -5, 3, 11/*mean (0.0224022), correlation (0.549667)*/,
        6, -9, 11, -13/*mean (0.029161), correlation (0.546295)*/,
        3, -1, 7, 12/*mean (0.0303081), correlation (0.548599)*/,
        11, -1, 12, 4/*mean (0.0355151), correlation (0.523943)*/,
        -3, 0, -3, 6/*mean (0.0417904), correlation (0.543395)*/,
        4, -11, 4, 12/*mean (0.0487292), correlation (0.542818)*/,
        2, -4, 2, 1/*mean (0.0575124), correlation (0.554888)*/,
        -10, -6, -8, 1/*mean (0.0594242), correlation (0.544026)*/,
        -13, 7, -11, 1/*mean (0.0597391), correlation (0.550524)*/,
        -13, 12, -11, -13/*mean (0.0608974), correlation (0.55383)*/,
        6, 0, 11, -13/*mean (0.065126), correlation (0.552006)*/,
        0, -1, 1, 4/*mean (0.074224), correlation (0.546372)*/,
        -13, 3, -9, -2/*mean (0.0808592), correlation (0.554875)*/,
        -9, 8, -6, -3/*mean (0.0883378), correlation (0.551178)*/,
        -13, -6, -8, -2/*mean (0.0901035), correlation (0.548446)*/,
        5, -9, 8, 10/*mean (0.0949843), correlation (0.554694)*/,
        2, 7, 3, -9/*mean (0.0994152), correlation (0.550979)*/,
        -1, -6, -1, -1/*mean (0.10045), correlation (0.552714)*/,
        9, 5, 11, -2/*mean (0.100686), correlation (0.552594)*/,
        11, -3, 12, -8/*mean (0.101091), correlation (0.532394)*/,
        3, 0, 3, 5/*mean (0.101147), correlation (0.525576)*/,
        -1, 4, 0, 10/*mean (0.105263), correlation (0.531498)*/,
        3, -6, 4, 5/*mean (0.110785), correlation (0.540491)*/,
        -13, 0, -10, 5/*mean (0.112798), correlation (0.536582)*/,
        5, 8, 12, 11/*mean (0.114181), correlation (0.555793)*/,
        8, 9, 9, -6/*mean (0.117431), correlation (0.553763)*/,
        7, -4, 8, -12/*mean (0.118522), correlation (0.553452)*/,
        -10, 4, -10, 9/*mean (0.12094), correlation (0.554785)*/,
        7, 3, 12, 4/*mean (0.122582), correlation (0.555825)*/,
        9, -7, 10, -2/*mean (0.124978), correlation (0.549846)*/,
        7, 0, 12, -2/*mean (0.127002), correlation (0.537452)*/,
        -1, -6, 0, -11/*mean (0.127148), correlation (0.547401)*/
};

// compute the descriptor
void computeORBDesc(const cv::Mat &image, vector<cv::KeyPoint> &keypoints, vector<DescType> &desc) {
    for (auto &kp: keypoints) {
        DescType d(256, false);
        double un_up,un_vp,un_uq,un_vq; // 一对点；
        double up,vp,uq,vq; // 旋转后的点；
        for (int i = 0; i < 256; i++) {
            // START YOUR CODE HERE (~7 lines)
            d[i] = 0;  // if kp goes outside, set d.clear()

            un_up = ORB_pattern[i*4];
            un_vp = ORB_pattern[i*4+1];
            un_uq = ORB_pattern[i*4+2];
            un_vq = ORB_pattern[i*4+3];           // 比较两组点的灰度值大小；

            // 旋转到主方向上；
            double angle = kp.angle * (pi/180);

            up =kp.pt.x+  cos(angle)*un_up-sin(angle)*un_vp;
            vp =kp.pt.y+ sin(angle)*un_up + cos(angle)*un_vp;
            uq =kp.pt.x+  cos(angle)*un_uq-sin(angle)*un_vq;
            vq =kp.pt.y+ sin(angle)*un_uq + cos(angle)*un_vq;

            //边界约束；
            if(up>image.cols||up<0 || vp <0||vp>image.rows||uq>image.cols||uq<0 || vq <0||vq>image.rows)
            {
                d.clear();//超出边界，特征点描述子清零；
                break;
            }
            else if(image.at<uchar>(vp,up)<image.at<uchar>(vq,uq))
            {
                d[i]=1;
            }

        // END YOUR CODE HERE
        }
        desc.push_back(d);
    }

    int bad = 0;
    for (auto &d: desc) {
        if (d.empty()) bad++;
    }
    cout << "bad/total: " << bad << "/" << desc.size() << endl;
    return;
}



// brute-force matching
void bfMatch(const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches) {
    int d_max = 50;
    int d = 0;
    int queryIdx,trainIdx;
    int dis;
    // START YOUR CODE HERE (~12 lines)
    // find matches between desc1 and desc2.
    for(int i =0;i<desc1.size();++i)
    {
        if(desc1[i].empty())
            continue;
        d=0;
        dis = 0;
        for(int j =0;j<desc2.size();++j)
        {
         if(desc2[j].empty())
             continue;
             d=0;
            for(int k = 0;k<256;++k)
            {
                if(desc1[i][k] != desc2[j][k])
                    d += 1;
            }
//            cout<<"d: "<<d<<endl;
            if (d<d_max&&(dis==0||d<dis))
            {
                dis = d;
                queryIdx = i;
                trainIdx = j;
            }
        }
        if(dis != 0) //匹配到了；
        {
            matches.push_back(cv::DMatch(queryIdx,trainIdx,dis));
        }

    }
    // END YOUR CODE HERE

    for (auto &m: matches) {
        cout << m.queryIdx << ", " << m.trainIdx << ", " << m.distance << endl;
    }
    return;
}